Question

if x4+1/x4 = 47 then x2 + 1/x2 =​

Answer 1

$\large\mathfrak \pink{Solution:-}$

$\underline \mathbb{GIVEN:-}$

${x}^{4} + \frac{1}{x {}^{4} } = 47$

$\underline \mathbb{TO \: FIND:-}$

${x}^{2} + \frac{1}{x {}^{2} }$

$\underline \mathbb{FORMULA:-}$

$(a + \frac{1}{a} ) {}^{2} = a {}^{2} + \frac{1}{ {a}^{2} } + 2 \times \cancel a \times \cancel\frac{1}{a} \\ \\ \implies \: a {}^{2} + \frac{1}{ {a}^{2} } + 2$

$\underline \mathbb{BY \: THE \: PROBLEM:-}$

${x}^{4} + \frac{1}{x {}^{4} } = 47 \\ \\ \implies \: ( {x}^{2} ) {}^{2} +( { \frac{1}{x {}^{2} } }) ^{2} = 47\\ \\ \implies \: ( {x}^{2} ) {}^{2} +( { \frac{1}{x {}^{2} } }) ^{2} + 2 = 47 + 2---(Add\:2\:both\: sides)\\ \\ \implies \:(x {}^{2} + \frac{ {1} }{x ^{2} }) {}^{2} = 49\\ \\ \implies (\:x {}^{2} + \frac{ 1 }{ {x}^{2} } )= \sqrt{49} \\ \\ \implies \:(\:x {}^{2} + \frac{ 1 }{ {x}^{2} } )= 7$

$\underline \mathbb{ANSWER:-}$

$\\ \implies \boxed{ \:(\:x {}^{2} + \frac{ 1 }{ {x}^{2} } ) = 7}$

Answer 2

the solution is given above.....